Page 284 - FUNDAMENTALS OF COMPUTER

NPP

284 Fundamentals of Computers NPP

+17 can be represented in 8-bit signed- (+17) H$mo 8-{~Q> gmBÝS> _op½ZQ²>`yS> _| BgàH$ma
magnitude form as 00010001. The represen- {bIm Om gH$Vm h¡ … 00010001. (-26) H$mo àmá
tation of –26 can be obtained from that of +26
(00011010) by taking two's complement of it : H$aZo Ho$ {bE nhbo (+ 26) H$m Vwë` àmá H$aVo h¢ Omo
Bg àH$ma h¡… 00011010 A~ Bg g§»`m H$m 2's
H$m°påßb_|Q> boZo na (-26) H$m Vwë` àmá hmoVm h¡ Omo Bg
àH$ma h¡… 11100110
–26 →11100110
Now, adding both the numbers: XmoZm| g§»`mAm| H$mo Omo‹S>Zo na…

+ 17 → 0001 0 00 1
− 26 →+ 11 10 0 1 1 0
1 1 1 10 11 1
Since MSB is 1 the result is a negative MSB Ho$ ñWmZ na 1 h¡ Omo ~VmVm h¡ {H$ n[aUm_
integer whose actual value can be obtained by F$UmË_H$ h¡ Am¡a `h gmBÝS> 2's H$m°påßb_|Q> _| Xem©`m
taking 2's complement of 11110111. This comes J`m h¡ Ÿ& BgH$m dmñV{dH$ _mZ 2's H$m°påßb_|Q> boZo na
as –00001001 which is –9 in decimal. Thus, the
result can be written as : OmZm Om gH$Vm h¡ Ÿ& Omo Bg àH$ma hmoJm- 00001001
`h Xe_bd _| - 9 h¡ Ÿ& AV… h_ {bI gH$Vo h¢ {H$…

(+17) + (–26) = (–9)
Note that (–9) will be saved in computer as ܶmZ aho {H$ H§$߶yQ>a ‘| (-9) H$mo 11110111
11110111. Ho$ ê$n ‘| hr god H$a|Jo&

Similarly we can perform addition if both {~ëHw$b Bgr Vah go Xmo F$UmË_H$ g§»`mAm| H$m `moJ
the numbers are negative. Just add after proper àmá H$a gH$Vo h¢Ÿ& g_w{MV ê$n go Vwë` {bIm| VWm
representation and neglect any end carry.
Omo‹S>H$a hm{gb H$mo N>mo‹S> XmoŸ&
Overflow Amodaâbmo
Sometimes the result cannot be fitted into H$^r-H$^r Cn`moJ H$s JB© {~Q>m| H$s g§»`m _| n[aUm_
the number of bits used. In that case the result g_m{hV Zht hmo nmVm h¡Ÿ& V~ n[aUm_ H$m _mZ VWm {MÝh
has a different magnitude and sign than the
desired. The points to be noted for overflow dmñV{dH$ go AbJ AmVm h¡Ÿ& Bg pñW{V H$mo Amodaâbmo
condition are: H$hVo h¢Ÿ& {H$Ýht Xmo gmBÝS> nyUmªH$m| H$mo Omo‹S>Zo na BZ Xmo
pñW{V`m| _| hr Amoìhaâbmo hmoVm h¡ …
1. When both the integers are of same sign. 1. XmoZm| g§»`mAm| Ho$ {MÝh g_mZ hmoŸ& Am¡a
and
2. Carry-in to the sign bit is different from 2. gmBZ {~Q> na AmZo dmbm hm{gb (C ) VWm BZgo
in
carry-out to the sign bit. ~mha OmZo dmbm hm{gb C XmoZm| AbJ-AbJ hmoŸ&
out
These two concepts are used by computer BZ Xmo pñW{V`m| go H$åß`yQ>a Amodaâbmo H$m nVm
circuit to detect the condition for overflow. For bJmVm h¡& bo{H$Z h_ Vmo AmgmZr go Amodaâbmo H$s pñW{V